Measurements.jl
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Introduction
What Is This Package Useful For?
Image credit: “xkcd: Error Bars” (CC-BY-NC
2.5)
Physical measures are typically reported with an error, a quantification of the
uncertainty of the
accuracy of the measurement. Whenever you perform mathematical operations
involving these quantities you have also to propagate the
uncertainty, so that
the resulting number will also have an attached error to quantify the confidence
about its accuracy.
Measurements.jl relieves you
from the hassle of propagating uncertainties coming from physical measurements,
when performing mathematical operations involving them. The linear error
propagation
theory
is employed to propagate the errors.
This library is written in Julia, a modern high-level,
high-performance dynamic programming language designed for technical computing.
When used in the Julia interactive
session, it can serve also as an
easy-to-use calculator.
Features List
- Support for most mathematical operations available in Julia standard library
and special functions
from
SpecialFunctions.jl
package, involving real and complex numbers. All existing functions that
accept AbstractFloat (and Complex{AbstractFloat} as well) arguments and
internally use already supported functions can in turn perform calculations
involving numbers with uncertainties without being redefined. This greatly
enhances the power of Measurements.jl without effort for the users
- Functional correlation between variables is correctly handled, so
x-x ≈ zero(x), x/x ≈ one(x), tan(x) ≈ sin(x)/cos(x), cis(x) ≈ exp(im*x),
etc…
- Support for
arbitrary precision
(also called multiple precision) numbers with uncertainties. This is useful
for measurements with very low relative error
- Define arrays of measurements and perform calculations with them. Some linear
algebra functions work out-of-the-box
- Propagate uncertainty for any function of real arguments (including functions
based on
C/Fortran calls),
using
@uncertain
macro
- Function to get the derivative and the gradient of an expression with respect
to one or more independent measurements
- Functions to calculate
standard score and
weighted mean
- Parse strings to create measurement objects
- Easy way to attach the uncertainty to a number using the
± sign as infix
operator. This syntactic sugar makes the code more readable and visually
appealing
- Extensible in combination with external packages: you can propagate errors of
measurements with their physical units, perform numerical integration
with
QuadGK.jl, numerical and
automatic differentiation, and much more.
- Integration with
Plots.jl.
The method used to handle functional correlation is described in this paper:
A current limitation of the package is that it is not yet possible to define
quantities related by a correlation matrix.
If you use use this package for your research, please cite it.
Documentation
The complete manual of Measurements.jl is available at
https://juliaphysics.github.io/Measurements.jl/stable/. There, people
interested in the details of the package, in order integrate the package in
their workflow, can find a technical appendix explaining how the package
internally works.
Installation
The latest version of Measurements.jl is available for Julia v1.0 and later
releases, and can be installed with Julia built-in package
manager. In a Julia session, after
entering the package manager mode with ], run the command
pkg> update
pkg> add Measurements
Older versions of this package are also available for Julia 0.4-0.7.
Usage
After installing the package, you can start using it with
using Measurements
The module defines a new Measurement data type. Measurement objects can be
created with the two following constructors:
measurement(value, uncertainty)
value ± uncertainty
where
value is the nominal value of the measurementuncertainty is its uncertainty, assumed to be a
standard deviation.
Here is a quick taster of the functionalities of the package:
julia> using Measurements
julia> a = measurement(4.5, 0.1)
4.5 ± 0.1
julia> b = 3.8 ± 0.4
3.8 ± 0.4
julia> 2a + b
12.8 ± 0.4472135954999579
julia> x = 8.4 ± 0.7
julia> x - x
0.0 ± 0.0
julia> x/x
1.0 ± 0.0
julia> x*x*x - x^3
0.0 ± 0.0
julia> sin(x)/cos(x) - tan(x)
-2.220446049250313e-16 ± 0.0 # They are equal within numerical accuracy
For more details about the use of the package read the
documentation, in
particular the
Usage and
Examples
sections.
License
The Measurements.jl package is licensed under the MIT “Expat” License. The
original author is Mosè Giordano.
Please, cite the paper Giordano 2016 (http://arxiv.org/abs/1610.08716) if you
employ this package in your research work. For your convenience, a BibTeX entry
is provided in the CITATION.bib file.
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